He said: “If Labour continues to support it, which they should and I believe they will, then of course it will have all-party support and it will proceed.”

He added: “If Labour are to run away from this they will be letting down the Midlands, they will be letting down the North, they will be kicking sand in the face of council leaders right across the country who want this to go ahead.

“They will be turning their backs on businesses who have been telling us how important it is that infrastructure projects like this go ahead.”

Up to 60 Conservatives are likely oppose the plans in the Commons, when MPs are set to vote on legislation to prepare the way for the development next week.

Mr Cameron said he would do all he could to win round a minority of Conservative MPs, many with constituencies on the route, who have been fighting the plans.

He said: “I will do everything I can to persuade MPs on all sides of the House that this is important and a good project.”

He added that the success of HS2 was vital to ensure that the economic recovery was equally shared by the north and south of the country.

He said: “This is an important national project. I want to see a recovery for the north and the south. I don’t want to see again a situation under Labour where for every 10 jobs created in the south there is only one created in the north.”

Mr Cameron was speaking after Mr Balls reiterated his concerns about the scheme in an interview on BBC Radio Five Live.

He said that there was “no blank cheque” and it was “completely irresponsible” that “even though the costs are going up billion by billion, and even though the benefits are becoming less clear, they are going to go ahead regardless”.

Last month, Mr Balls questioned whether the HS2 rail project was “the best way to spend £50bn for the future of our country” - leading some to speculate that a Labour government would cancel it if costs rose.

Earlier this week Lord Mandelson, a former Business secretary, branded it a “political trophy project” and warned that it was “flimsy evidence” and would “suck the very life blood” out of the rest of the country’s rail network.